9514 1404 393
Answer:
4) 6x
5) 2x +3
Step-by-step explanation:
We can work both these problems at once by finding an applicable rule.
where O(h²) is the series of terms involving h² and higher powers. When divided by h, each term has h as a multiplier, so the series sums to zero when h approaches zero. Of course, if n < 2, there are no O(h²) terms in the expansion, so that can be ignored.
This can be referred to as the <em>power rule</em>.
Note that for the quadratic f(x) = ax^2 +bx +c, the limit of the sum is the sum of the limits, so this applies to the terms individually:
lim[h→0](f(x+h)-f(x))/h = 2ax +b
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4. The gradient of 3x^2 is 3(2)x^(2-1) = 6x.
5. The gradient of x^2 +3x +1 is 2x +3.
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If you need to "show work" for these problems individually, use the appropriate values for 'a' and 'n' in the above derivation of the power rule.
Answer:
x = 4.
Step-by-step explanation:
log(x + 6)- log(x - 3) = 1
Using the law log a - log b = log a/b:
log (x + 6)/ (x - 3) = 1
Removing logs:
(x + 6)/ (x - 3) = 10
x+ 6 = 10x - 30
9x = 36
x = 4 (answer).
Answer:
80 < 93 < 121 < 127
Step-by-step explanation:
For a geometric series,
Formula to be used,
Sum of t terms of a geometric series = 
Here t = number of terms
a = first term
r = common ratio
1). 
First term of this series 'a' = 3
Common ratio 'r' = 2
Number of terms 't' = 5
Therefore, sum of 5 terms of the series = 
= 93
2). 
First term 'a' = 1
Common ratio 'r' = 2
Number of terms 't' = 7
Sum of 7 terms of this series = 
= 127
3). 
First term 'a' = 1
Common ratio 'r' = 3
Number of terms 't' = 5
Therefore, sum of 5 terms = 
= 121
4). 
First term 'a' = 2
Common ratio 'r' = 3
Number of terms 't' = 4
Therefore, sum of 4 terms of the series = 
= 80
80 < 93 < 121 < 127 will be the answer.
